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The Surface to Volume Ratio (SA:V) of a Great Stellated Dodecahedron is the numerical ratio of its total surface area to its volume. It's an important geometric property that indicates how much surface area is available per unit volume of the polyhedron.
The calculator uses the formula:
Where:
Explanation: The formula calculates the ratio by dividing the constant expression (3√3√(5+2√5)) by the circumradius of the polyhedron.
Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and physics. For polyhedra, it helps understand properties related to surface area efficiency and volume containment.
Tips: Enter the circumradius of the Great Stellated Dodecahedron in meters. The value must be positive and greater than zero for valid calculation.
Q1: What is a Great Stellated Dodecahedron?
A: It's a Kepler-Poinsot polyhedron that represents one of the four regular star polyhedra, formed by extending the faces of a regular dodecahedron.
Q2: Why is surface to volume ratio important?
A: It indicates how much surface area is available relative to the volume, which affects properties like heat transfer, chemical reactivity, and structural efficiency.
Q3: What units are used for the calculation?
A: The circumradius should be in meters (m), and the resulting SA:V ratio will be in inverse meters (m⁻¹).
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Great Stellated Dodecahedron. Other polyhedra have different surface to volume ratio formulas.
Q5: What if I have the edge length instead of circumradius?
A: You would need to convert edge length to circumradius using the appropriate conversion formula for the Great Stellated Dodecahedron before using this calculator.